Context-Dependent Data Envelopment Analysis with Interval Data
Mohammad Izadikhah
DOI: 10.4236/ajcm.2011.14031   PDF    HTML     7,640 Downloads   12,516 Views   Citations


Data envelopment analysis (DEA) is a non-parametric method for evaluating the relative efficiency of decision making units (DMUs) on the basis of multiple inputs and outputs. The context-dependent DEA is introduced to measure the relative attractiveness of a particular DMU when compared to others. In real-world situation, because of incomplete or non-obtainable information, the data (Input and Output) are often not so deterministic, therefore they usually are imprecise data such as interval data, hence the DEA models becomes a nonlinear programming problem and is called imprecise DEA (IDEA). In this paper the context-dependent DEA models for DMUs with interval data is extended. First, we consider each DMU (which has interval data) as two DMUs (which have exact data) and then, by solving some DEA models, we can find intervals for attractiveness degree of those DMUs. Finally, some numerical experiment is used to illustrate the proposed approach at the end of paper.

Share and Cite:

Izadikhah, M. (2011) Context-Dependent Data Envelopment Analysis with Interval Data. American Journal of Computational Mathematics, 1, 256-263. doi: 10.4236/ajcm.2011.14031.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] A. Charnes, W. W.Cooper and E. Rhodes, “Measuring the Efficiency of Decision Making Units,” European Journal of Operational Research, Vol. 2, No. 6, 1978, pp. 429- 444. doi:10.1016/0377-2217(78)90138-8
[2] H. Morita, K. Hirokawa and J. Zhu, “A Slack-Based Mea- sure of Efficiency in Context Dependent Data Envelop- ment Analysis,” Omega, Vol. 33, No. 4, 2005, pp. 357- 362. doi:10.1016/
[3] L. M. Seiford and J. Zhu, “Context-Dependent Data En- velopment Analysis: Measuring Attractiveness and Pro- gress,” Omega, Vol. 31, No. 5, 2003, pp. 397-408. doi:10.1016/S0305-0483(03)00080-X
[4] J. Zhu, “Quantitative Models for Performance Evaluation and Benchmarking-Data Envelopment Analysis with Spread- sheets and DEA Excel Solver,” Kluwer, Boston, 2002.
[5] W. W. Cooper, K. S. Park and G. Yu, “IDEA and AR- IDEA: Models for Dealing with Imprecise Data in DEA,” Management Science, Vol. 45, No. 4, 1999, pp. 597-607. doi:10.1287/mnsc.45.4.597
[6] S. H. Kim, C. G. Park and K. S. Park, “An Application of Data Envelopment Analysis in Telephone Offices Evalu- ation with Partial Data,” Computers and Operations Re- search, Vol. 26, No. 1, 1999, pp. 59-72. doi:10.1016/S0305-0548(98)00041-0
[7] W. D. Cook, M. Kress and L. Seiford, “Data Envelopment Analysis in the Presence of Both Quantitative and Quali- tative Factors,” Journal of the Operational Research So- ciety, Vol. 47, No. 7, 1996, pp. 945-953.
[8] W. D. Cook, M. Kress and L. Seiford, “On the Use of Ordinal Data in Data Envelopment Analysis,” Journal of the Operational Research Society, Vol. 44, No. 2, 1993, pp. 133-140.
[9] W. D. Cook, J. Doyle, R. Green and M. Kress, “Multiple Criteria Modeling and Ordinal Data: Evaluation in Terms of Subset of Criteria,” European Journal of Operational Research, Vol. 98, No. 3, 1997, pp. 602-609. doi:10.1016/S0377-2217(96)00069-0
[10] J. Sarkis and S. Talluri, “A Decision Model for Evalua- tion of Flexible Manufacturing Systems in the Presence of Both Cardinal and Ordinal Factors,” International Journal of Production Research, Vol. 37, No. 13, 1999, pp. 2927-2938. doi:10.1080/002075499190356
[11] D. K. Despotis and Y. G. Smirlis, “Data Envelopment Ana- lysis with Imprecise Data,” European Journal of Operational Research, Vol. 140, No. 1, 2002, pp. 24-36. doi:10.1016/S0377-2217(01)00200-4
[12] G. R. Jahanshahloo, F. Hosseinzadeh Lotfi and M. Moradi, “Sensitivity and Stability Analysis in DEA with interval Data,” Applied Mathematics and Computation, Vol. 156, No. 2, 2004, pp. 463-477. doi:10.1016/j.amc.2003.08.005
[13] M. Izadikhah and F. Hosseinzadeh Lotfi, “Sensitivity Ana- lysis of Units with Interval Data in DEA,” International Mathematical Forum, No. 2, Vol. 42, 2007, pp. 2083-2097.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.